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t_{n}  for the sequence 2,9,28,65,126,.............is

Option: 1

t_{n}=n^{2}+1

 

 


Option: 2

t_{n}=n^{3}-2


Option: 3

t_{n}=n^{3}+1


Option: 4

None of these.


Answers (1)

best_answer

By observation

\begin{aligned} &t_{1}=1^{3}+1 \\ &t_{2}=2^{3}+1 \\ &t_{3}=3^{3}+1 \\ \end{aligned} and so on

\begin{aligned} &\cdots \cdot \cdot \\ \end{aligned}

So,\begin{aligned} &t_{n}=n^{3}+1 \end{aligned}

Alternate method

Checking options

(a) \begin{aligned} &t_{1}=1^{2}+1=2 \end{aligned}

     \begin{aligned} &t_{2}=2^{2}+1=5 \end{aligned} so, wrong

Similary other options may be checked.

Posted by

Gaurav

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